Theorems · Theorem · algebraic topology
simplyConnectedSpace_iff
∀ (X : Type u_3) [inst : TopologicalSpace X], SimplyConnectedSpace X ↔ Nonempty (FundamentalGroupoid X ≌ CategoryTheory.Discrete Unit)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CategoryTheory.Discretestatement and proof · cited by 2,447
- CategoryTheory.Equivalencestatement and proof · cited by 601
- FundamentalGroupoidstatement and proof · cited by 60
- SimplyConnectedSpacestatement and proof · cited by 19
- SimplyConnectedSpace.casesOnproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- simply_connected_defproof · cited by 0